Chapter 3 Homework Solutions
Questions for Review
1. The production possibilities frontier will be linear if the opportunity cost of producing a good
is constant no matter how much of that good is produced. This will be most likely if the good
is not produced using specialized inputs.
2. Absolute advantage reflects a comparison of the productivity of one person, firm, or nation to
that of another, while comparative advantage is based on the relative opportunity costs of
the persons, firms, or nations. While a person, firm, or nation may have an absolute
advantage in the production of every good, they cannot have a comparative advantage in the
production of every good.
3. Many examples are possible. Suppose, for example, that Roger can prepare a meal of hot
dogs and macaroni in just 10 minutes, while it takes Anita 20 minutes. Also suppose that
Roger can do all the laundry in 3 hours, while it takes Anita 4 hours. Roger has an absolute
advantage in both cooking and doing the laundry, but Anita has a comparative advantage in
doing the laundry. For Anita, the opportunity cost of doing the laundry is 12 meals; for
Roger, it is 18 meals.
4. Comparative advantage is more important for trade than absolute advantage. In the example
in Problem 3, Anita and Roger will complete their chores more quickly if Anita does at least
some of the laundry and Roger cooks the meals for both, because Anita has a comparative
advantage in doing the laundry, while Roger has a comparative advantage in cooking.
5. In order for trade to benefit both parties, the price for the trade must lie between the parties’
opportunity costs.
6. Economists oppose policies that restrict trade among nations because trade allows all
countries to achieve greater prosperity by allowing them to receive the gains from
comparative advantage. Restrictions on trade can hurt all countries.
Quick Check Multiple Choice
1. d
2. b
3. a
4. d
5. b
6. d
Problems and Applications
1. a. See Figure 2. If Maria spends all 5 hours studying economics, she can read 100 pages, so
that is the vertical intercept of the production possibilities frontier. If she spends all 5
hours studying sociology, she can read 250 pages, so that is the horizontal intercept. The
opportunity costs are constant, so the production possibilities frontier is a straight line.
Figure 2
b. It takes Maria 2 hours to read 100 pages of sociology. In that time, she could read 40
pages of economics. So the opportunity cost of 100 pages of sociology is 40 pages of
economics.
2. a.
U.S.
Japan
Workers needed to make:
One Car
One Ton of Grain
1/4
1/10
1/4
1/5
b. See Figure 3. With 100 million workers and 4 cars per worker, if either economy were
devoted completely to cars, it could make 400 million cars. Because a U.S. worker can
produce 10 tons of grain, if the United States produced only grain it would produce 1,000
million tons. Because a Japanese worker can produce 5 tons of grain, if Japan produced
only grain it would produce 500 million tons. These are the intercepts of the production
possibilities frontiers shown in the figure. Note that because the trade-off between cars
and grain is constant for both countries, the production possibilities frontiers are straight
lines.
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Figure 3
c.
Because a U.S. worker produces either 4 cars or 10 tons of grain, the opportunity cost of
one car is 2 1/2 tons of grain, which is 10/4. Similarly, the U.S. opportunity cost of a ton
of grain is 2/5 car (4 divided by 10). Because a Japanese worker produces either 4 cars
or 5 tons of grain, the opportunity cost of one car is 1 1/4 tons of grain, which is 5/4 and
the Japanese opportunity cost of a ton of grain is 4/5 car. This results in the following
table:
U.S.
Japan
Opportunity Cost of:
One Car (in terms of tons
One Ton of Grain (in
of grain given up)
terms of cars given up)
2 1/2
2/5
1 1/4
4/5
d. Neither country has an absolute advantage in producing cars, because they are equally
productive (the same output per worker); the United States has an absolute advantage
in producing grain, because it is more productive (greater output per worker).
e. Japan has a comparative advantage in producing cars, because it has a lower
opportunity cost in terms of grain given up. The United States has a comparative
advantage in producing grain, because it has a lower opportunity cost in terms of cars
given up.
f.
With half the workers in each country producing each of the goods, the United States
would produce 200 million cars (50 million workers times 4 cars each) and 500 million
tons of grain (50 million workers times 10 tons each). Japan would produce 200 million
cars (50 million workers times 4 cars each) and 250 million tons of grain (50 million
workers times 5 tons each).
g. From any situation with no trade, in which each country is producing some cars and
some grain, suppose the United States changed one worker from producing cars to
producing grain. That worker would produce 4 fewer cars and 10 additional tons of grain.
Then suppose the United States offers to trade 7 tons of grain to Japan for 4 cars. The
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United States will do this because the cost of producing 4 cars in the United States is 10
tons of grain. By trading, the United States can gain 4 cars for a cost of only 7 tons of
grain, so it is better off by 3 tons of grain. Suppose Japan changes one worker from
producing grain to producing cars. That worker would produce 4 more cars and 5 fewer
tons of grain. Japan will take the trade because it values 4 cars at 5 tons of grain, so it
will be better off by 2 tons of grain. With the trade and the change of one worker in both
the United States and Japan, each country gets the same amount of cars as before and
both get additional tons of grain (3 for the United States and 2 for Japan). Thus, by
trading and changing their production, both countries are better off.
3. a. Pat's opportunity cost of making a pizza is 1/2 gallon of root beer, because she could
brew 1/2 gallon in the time (2 hours) it takes her to make a pizza. Kris's opportunity cost
of making a pizza is 2/3 gallon of root beer, because she could brew 2/3 of a gallon in
the time (4 hours) it takes her to make a pizza. Pat has an absolute advantage in making
pizza because she can make one in 2 hours, while it takes Kris 4 hours. Because Pat's
opportunity cost of making pizza is less than Kris', Pat has a comparative advantage in
making pizza.
b. Because Pat has a comparative advantage in making pizza, she will make pizza and
exchange it for root beer that Kris makes.
c.
The highest price of pizza in terms of root beer that will make both roommates better off
is 2/3 of a gallon of root beer. If the price were higher than that, then Kris would prefer
making her own pizza (at an opportunity cost of 2/3 of a gallon of root beer) rather than
trading for pizza that Pat makes. The lowest price of pizza in terms of root beer that will
make both roommates better off is 1/2 gallon of root beer. If the price were lower than
that, then Pat would prefer making her own root beer (she can make 1/2 gallon of root
beer instead of making a pizza) rather than trading for root beer that Kris makes.
4. a. Because a Canadian worker can make either 2 cars a year or 30 bushels of wheat, the
opportunity cost of a car is 15 bushels of wheat. Similarly, the opportunity cost of a
bushel of wheat is 1/15 of a car. The opportunity costs are the reciprocals of each other.
b. See Figure 4. If all 10 million workers produce 2 cars each, they produce a total of 20
million cars, which is the vertical intercept of the production possibilities frontier. If all 10
million workers produce 30 bushels of wheat each, they produce a total of 300 million
bushels, which is the horizontal intercept of the production possibilities frontier. Because
the trade-off between cars and wheat is always the same, the production possibilities
frontier is a straight line.
If Canada chooses to consume 10 million cars, it will need 5 million workers devoted to
car production. That leaves 5 million workers to produce wheat, who will produce a total
of 150 million bushels (5 million workers times 30 bushels per worker). This is shown as
point A on Figure 4.
c.
If the United States buys 10 million cars from Canada and Canada continues to consume
10 million cars, then Canada will need to produce a total of 20 million cars. So Canada
will be producing at the vertical intercept of the production possibilities frontier.
However, if Canada gets 20 bushels of wheat per car, it will be able to consume 200
million bushels of wheat, along with the 10 million cars. This is shown as point B in the
figure. Canada should accept the deal because it gets the same number of cars and 50
million more bushes of wheat.
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Figure 4
5. a. English workers have an absolute advantage over Scottish workers in producing scones,
because English workers produce more scones per hour (50 vs. 40). Scottish workers
have an absolute advantage over English workers in producing sweaters, because
Scottish workers produce more sweaters per hour (2 vs. 1). Comparative advantage runs
the same way. English workers, who have an opportunity cost of 1/50 sweater per scone
(1 sweater per hour divided by 50 scones per hour), have a comparative advantage in
scone production over Scottish workers, who have an opportunity cost of 1/20 sweater
per scone (2 sweaters per hour divided by 40 scones per hour). Scottish workers, who
have an opportunity cost of 20 scones per sweater (40 scones per hour divided by 2
sweaters per hour), have a comparative advantage in sweater production over English
workers, who have an opportunity cost of 50 scones per sweater (50 scones per hour
divided by 1 sweater per hour).
b. If England and Scotland decide to trade, Scotland will produce sweaters and trade them
for scones produced in England. A trade with a price between 20 and 50 scones per
sweater will benefit both countries, as they will be getting the traded good at a lower
price than their opportunity cost of producing the good in their own countries.
c.
Even if a Scottish worker produced just one sweater per hour, the countries would still
gain from trade, because Scotland would still have a comparative advantage in producing
sweaters. Its opportunity cost for sweaters would be higher than before (40 scones per
sweater, instead of 20 scones per sweater before). But there are still gains from trade
because England has a higher opportunity cost (50 scones per sweater).
6. a. With no trade, 1 pair of white socks trades for 1 pair of red socks in Boston, because
productivity is the same for the two types of socks. The price in Chicago is 2 pairs of red
socks per 1 pair of white socks.
b. Boston has an absolute advantage in the production of both types of socks, because a
worker in Boston produces more (3 pairs of socks per hour) than a worker in Chicago (2
pairs of red socks per hour or 1 pair of white socks per hour).
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Chicago has a comparative advantage in producing red socks, because the opportunity
cost of producing a pair of red socks in Chicago is 1/2 pair of white socks, while the
opportunity cost of producing a pair of red socks in Boston is 1 pair of white socks.
Boston has a comparative advantage in producing white socks, because the opportunity
cost of producing a pair of white socks in Boston is 1 pair of red socks, while the
opportunity cost of producing a pair of white socks in Chicago is 2 pairs of red socks.
c.
If they trade socks, Boston will produce white socks for export, because it has the
comparative advantage in white socks, while Chicago produces red socks for export,
which is Chicago's comparative advantage.
d. Trade can occur at any price between 1 and 2 pairs of red socks per pair of white socks.
At a price lower than 1 pair of red socks per pair of white socks, Boston will choose to
produce its own red socks (at a cost of 1 pair of red socks per pair of white socks)
instead of buying them from Chicago. At a price higher than 2 pairs of red socks per pair
of white socks, Chicago will choose to produce its own white socks (at a cost of 2 pairs of
red socks per pair of white socks) instead of buying them from Boston.
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7. a. Gains from trade will be possible when X does not equal 3. Gains from trade are possible
when a comparative advantage exists. The opportunity cost of 1 car in Germany is 200
cases of wine (400 hours/2 hours per case of wine). Likewise, the opportunity cost of 1
case of wine in Germany is 1/200 car. When X=3, the opportunity cost of 1 car in
France is 200 cases of wine (600 hours/3 hours per case of wine). In this instance,
neither country has a comparative advantage. At all other values of X, a comparative
advantage will exist.
b. Germany will export cars and import wine for all values of X<3. For Germany to export
cars, it must have the comparative advantage in producing cars and France must have
the comparative advantage in producing wine. This occurs when Germany has a smaller
opportunity cost of producing cars than France does. We know the opportunity cost of 1
car in Germany is 200 cases of wine. When X<3, the opportunity cost of 1 car in France
is greater than 200 cases of wine. For example, when X=2, the opportunity cost of 1 car
in France is 300 cases of wine (600 hours/2 hours per case = 300 cases). Therefore,
Germany will have the comparative advantage in cars, export cars and import wine for all
values of X<3.
8. a. The production possibilities frontiers for the two countries are shown in Figure 5. If,
without trade, a U.S. worker spends half of his time producing each good, the United
States will have 50 shirts and 10 computers. If, without trade, a worker in China spends
half of his time producing each good, China will have 50 shirts and 5 computers.
Figure 5
b. China would export shirts because it has the lower opportunity cost of shirts. For China,
the opportunity cost of 1 shirt is 1/10 computer. For the United States, the opportunity
cost of a shirt is 1/5 computer. Therefore, China has a comparative advantage in the
production of shirts and the United States has a comparative advantage in the production
of computers.
The price of a shirt will fall between 1/5 and 1/10 of a computer. An example would be a
price of 1/7 computer. Suppose China produced only shirts (100 shirts) and exported 50
shirts in exchange for 7.14 computers (50/7 = 7.14). This trade makes China better off
than it was before trade (50 shirts and 5 computers). The United States would also
benefit from this trade. If the United States produced only computers (20 computers),
and traded 7.14 of them to China for 50 shirts, the United States would have 12.86 (207.14) computers and 50 shirts and would be better off than before trade (10 computers
and 50 shirts).
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c.
The price of a computer would fall between 5 and 10 shirts. If the price were below 5,
the United States would not be willing to export computers because the opportunity cost
of a shirt for the United States is 1/5 computer. If the price were greater than 10 shirts,
China would not be willing to import computers because (for China) the opportunity cost
of a computer is 10 shirts.
d. Once the productivity is the same in the two countries, the benefits of trade disappear.
Trade is beneficial because it allows countries to exploit their comparative advantage. If
China and the United States have exactly the same opportunity cost of producing shirts
and computers, there will be no more gains from trade available.
9. a. True; two countries can achieve gains from trade even if one of the countries has an
absolute advantage in the production of all goods. All that is necessary is that each
country has a comparative advantage in some good.
b. False; no one can have a comparative advantage in everything. Comparative advantage
reflects the opportunity cost of one good or activity in terms of another. If you have a
comparative advantage in one thing, you must have a comparative disadvantage in the
other thing.
c.
False; trades can and do benefit both sidesespecially trades based on comparative
advantage. If both sides did not benefit, trades would never occur.
d. False; to be good for both parties, the trade price must lie between the two opportunity
costs.
e. False; trade that makes the country better off can harm certain individuals in the
country. For example, suppose a country has a comparative advantage in producing
wheat and a comparative disadvantage in producing cars. Exporting wheat and importing
cars will benefit the nation as a whole, as it will be able to consume more of both goods.
However, the introduction of trade will likely be harmful to domestic auto workers and
manufacturers.
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